Bilaterally asymmetric design for minimizing wave drag

ABSTRACT

An air vehicle may include a body having forwardly-swept fixed wings or unswept fixed wings. The body may have a longitudinal axis continuously oriented parallel to a forward flight direction when the air vehicle is in flight. The air vehicle may include at least one of the following components being mounted on opposite sides of the body: longitudinally offset engine nacelles, asymmetrically lengthened engine nacelles, and longitudinally offset protruding aerodynamic surfaces comprising at least one of stabilizers, canards, empennage control surfaces, external stores, and high aspect ratio wings.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation-in-part application of andclaims priority to pending U.S. application Ser. No. 13/687,483 filed onNov. 28, 2012, and entitled SYSTEM AND METHOD FOR MINIMIZING WAVE DRAGTHROUGH BILATERALLY ASYMMETRIC DESIGN, the entire contents of which isexpressly incorporated by reference herein.

FIELD

The present disclosure relates generally to aircraft configurations and,more particularly, to configurations for minimizing wave drag of an airvehicle.

BACKGROUND

Wave drag is a phenomenon that occurs as a result of the compression ofair as an aircraft approaches the speed of sound. The compressiongenerates a shock wave which may be accompanied by a localized change inthe pressure and/or temperature of the air. At subsonic speeds, wavedrag forms a relatively small portion of the overall aerodynamic drag onan aircraft. However, wave drag increases significantly as an aircraftapproaches Mach 1.

Known methods of minimizing wave drag include designing an aircraft witha configuration that follows the Whitcomb Area Rule. The Whitcomb AreaRule dictates a minimization of change in the cross-sectional area ofthe aircraft in the longitudinal direction. In this regard, an aircraftfollowing the Whitcomb Area Rule has a relatively smooth or gradualchange in the size of the cross-sectional area regardless of changes inthe cross-sectional shape. In conventional aircraft, the forward end ofan aircraft fuselage may have a relatively small cross-sectional area.Unfortunately, the cross-sectional area may increase significantly andabruptly at the wings and/or engines and which may result in significantwave drag at transonic speeds.

Attempts to minimize changes in the longitudinal cross-sectional area ofan aircraft including locally necking down the fuselage at the juncturewith the wings to minimize the change in total cross-sectional area atthat location. Unfortunately, designing and manufacturing an aircraftwith a fuselage having a variable cross-sectional shape adds to theoverall cost and complexity of the aircraft. In addition, in acommercial airliner, locally necking down the fuselage at the wings maybe economically undesirable due the potential loss of revenue-generatingpassenger seats or cargo space.

Another approach to minimizing wave drag in an aircraft is by formingthe wings in a swept arrangement. Wing sweep may minimize changes in thelongitudinal cross-sectional area of an aircraft by distributing thecross-sectional area of the wings over a longer length of the fuselage.Wing sweep may delay the onset of wave drag rise by increasing the Machnumber required to generate shockwaves on the wing surface. The increasein Mach number may occur due to alignment of the pressure isobars withthe sweep of the wing such that shocks will only form when the componentof velocity perpendicular to the pressure isobars reaches sonic speeds.Unfortunately, excessive wing sweep may have an effect on the low speedperformance of an aircraft. In addition, wing sweep may add cost andcomplexity to the aircraft design and manufacturing process.

For aircraft operating at subsonic speeds, wave drag accounts for arelatively small portion of the total aerodynamic drag of the aircraft,as indicated above. However, a small reduction in wave drag maytranslate into a significant increase in fuel efficiency of theaircraft. Military aircraft that operate in the transonic region mayalso benefit from a reduction in wave drag with an increase in top speedand/or an increase in range.

As can be seen, there exists a need in the art for an aircraftconfiguration that minimizes wave drag and which may be provided withminimal impact on the aircraft design and manufacturing process.

SUMMARY

The above-noted needs associated with minimizing wave drag arespecifically addressed and alleviated by the present disclosure whichprovides an air vehicle having a bilaterally asymmetric configuration.The air vehicle may include a body having forwardly-swept fixed wings orunswept fixed wings. The body may have a longitudinal axis continuouslyoriented parallel to a forward flight direction when the air vehicle isin flight. The air vehicle may include at least one of the followingcomponents being mounted on opposite sides of the body: longitudinallyoffset engine nacelles, asymmetrically lengthened engine nacelles, andlongitudinally offset protruding aerodynamic surfaces comprising atleast one of stabilizers, canards, empennage control surfaces, externalstores, and high aspect ratio wings.

In a further embodiment, the air vehicle may have a bilaterallyasymmetric configuration. The air vehicle may include fixed wings and alongitudinal axis continuously oriented parallel to a forward flightdirection when the air vehicle is in flight. The air vehicle may includea forward nacelle and an aft nacelle mounted on opposite sides of thebody. An engine inlet of the aft nacelle may be located aft of theengine inlet of the forward nacelle by no more than 20 percent of anengine length of the forward nacelle.

Also disclosed is a method of minimizing wave drag of an air vehicle.The method may include providing a body of an air vehicle havingforwardly-swept fixed wings or unswept fixed wings, and having alongitudinal axis oriented generally parallel to a forward flightdirection. The method may also include longitudinally offsetting atleast one of the following components on opposite sides of the bodyrelative to the longitudinal axis: engine nacelles, and protrudingaerodynamic surfaces such as stabilizers, canards, empennage controlsurfaces, external stores, and high aspect ratio wings.

In a further embodiment, disclosed is a method of minimizing wave dragof an air vehicle. The method may include providing a body having fixedwings and a longitudinal axis continuously oriented parallel to aforward flight direction when the air vehicle is in flight. The methodmay also include mounting a forward nacelle and an aft nacelle onopposite sides of the body. In addition, the method may also includelocating an engine inlet of the aft nacelle aft of the engine inlet ofthe forward nacelle by no more than 20 percent of an engine length ofthe forward nacelle.

The features, functions and advantages that have been discussed can beachieved independently in various embodiments of the present disclosureor may be combined in yet other embodiments, further details of whichcan be seen with reference to the following description and drawingsbelow.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features of the present disclosure will become moreapparent upon reference to the drawings wherein like numbers refer tolike parts throughout and wherein:

FIG. 1 is a top view of a baseline configuration of an aircraft having abilaterally symmetric arrangement;

FIG. 1A is a diagrammatic section view of a local longitudinalcross-sectional area of the baseline configuration of the aircraft ofFIG. 1 taken along a cutting plane at a forward station location of theaircraft;

FIG. 1B is a diagrammatic section view of a local longitudinalcross-sectional area of the baseline configuration taken along a cuttingplane at an intermediate station location;

FIG. 1C is a diagrammatic section view of a local longitudinalcross-sectional area of the baseline configuration taken along a cuttingplane at an aft station location;

FIG. 2 is a top view of an aircraft in a bilaterally asymmetricarrangement having an engine offset configuration;

FIG. 2A is a diagrammatic section view of a local longitudinalcross-sectional area of the engine offset configuration of the aircraftof FIG. 2 taken along a cutting plane at the forward station location;

FIG. 2B is a diagrammatic section view of a local longitudinalcross-sectional area of the engine offset configuration taken along acutting plane at a first intermediate station location;

FIG. 2C is a diagrammatic section view of a local longitudinalcross-sectional area of the engine offset configuration taken along acutting plane at a second intermediate station location;

FIG. 2D is a diagrammatic section view of a local longitudinalcross-sectional area of the engine offset configuration taken along acutting plane at the aft station location;

FIG. 3 is a graph plotting longitudinal cross-sectional area versusstation location of a baseline aircraft configuration and an engineoffset aircraft configuration;

FIG. 4 is a graph plotting change in cross-sectional area versus stationlocation for the cross-sectional area plots of the baselineconfiguration and the engine offset configuration of FIG. 3;

FIG. 5 is a top view of an embodiment of an aircraft in a bilaterallyasymmetric configuration having offset wings and offset horizontalstabilizers;

FIG. 6 is a top view of an embodiment of an aircraft in a bilaterallyasymmetric configuration having forward and aft nacelle extensionsmounted to the engine nacelles on opposite sides of the aircraft;

FIG. 7A is a top view of an embodiment of a cruise missile in abilaterally symmetric configuration;

FIG. 7B is a top view of the cruise missile of FIG. 7A in a bilaterallyasymmetric configuration having offset missile wings;

FIG. 8A is a top view of an embodiment of an aircraft having externalstores mounted in a bilaterally symmetric configuration;

FIG. 8B is a top view of the aircraft of FIG. 8A wherein a first one ofthe external stores is released on one side of the fuselage and on anoutboard side of the wing;

FIG. 8C is a top view of the aircraft of FIG. 8B wherein a second one ofthe external stores is released on an opposite side of the fuselage fromFIG. 8B and on an inboard side of the wing;

FIG. 8D is a top view of the aircraft of FIG. 8C wherein a third one ofthe external stores is released from the same side of the fuselage as inFIG. 8C;

FIG. 8E is a top view of an embodiment of an aircraft having externalstores mounted in a bilaterally asymmetric configuration;

FIG. 9 is a flow diagram having one or more operation that may beincluded in a method of minimizing wave drag of an air vehicle;

FIG. 10 is a graph plotting a ratio of wave drag coefficient/minimumdrag versus offset distance as a percentage of a maximum offset distancefor a bilaterally asymmetric configuration of an aircraft having offsetwings, offset engines, and offset engine nacelle lengths; and

FIG. 11 is a top view of an aircraft in a bilaterally asymmetricconfiguration wherein the engine inlet of the aft nacelle is located aftof the engine inlet of the forward nacelle by no more than 20 percent ofan engine length of the forward nacelle.

DETAILED DESCRIPTION

Referring now to the drawings wherein the showings are for purposes ofillustrating various embodiments of the present disclosure, shown inFIG. 1 is a top view of an air vehicle 100 configured as an aircraft 102or airplane. The aircraft 102 is illustrated as a tube-and-wing aircraft102 or airplane and is shown in a baseline configuration 132 wherein theaircraft components 114 are arranged in a bilaterally symmetricconfiguration 130 relative to a longitudinal axis 106 of the aircraft102. The aircraft 102 may be arranged such that the longitudinal axis106 of the body 104 is oriented generally parallel to a forward flightdirection 112 of the aircraft 102 corresponding to a direction of anoncoming airflow stream 110.

The body 104 of the aircraft 102 may comprise a fuselage 170 extendingfrom a fuselage forward end 172 to a fuselage aft end 174. The fuselageaft end 174 may include an empennage 260. The empennage 260 may includeone or more tail surfaces such as one or more stabilizers 268 and/orcontrol surfaces. For example, the empennage 260 may include horizontalstabilizers 268, one or more vertical stabilizers 262, and one or morecontrol surfaces 272 such as an elevator (not shown) and/or a rudder(not shown) for directional control of the aircraft 102. In the baselineconfiguration 132 of the aircraft 102 in FIG. 1, the stabilizers 268 arearranged in a bilaterally symmetric configuration 130 wherein thehorizontal stabilizers 268 are positioned at the same station locationand are generally longitudinally aligned with one another.

In FIG. 1, the aircraft 102 may further include one or more protrudingaerodynamic surfaces 190 that may extend outwardly from the body 104 orfuselage 170. For example, the aircraft 102 may include a pair of wings192 that may be mounted on opposite sides of the fuselage 170. The wings192 on each side of the fuselage 170 may be configured substantiallysimilar to one another. For example, the wings 192 on each side of thefuselage 170 may generally have the same size, shape, contour, airfoilsections, wing span, taper ratio, sweep (e.g., forward or aft), anddihedral or anhedral. Although shown in an aftwardly swept and taperedconfiguration, the wings 192 may be provided in a non-sweptconfiguration or a forwardly-swept configuration. In addition, the wings192 may be provided in a non-tapered configured wherein the airfoilsection (not shown) or chord is generally constant along a semi-span ofeach wing 192.

In embodiments of the system and method disclosed herein, the wings 192may be provided as high aspect ratio wings 192. For example, the highaspect ratio wings 192 may have an aspect ratio of wingspan (not shown)to average chord (not shown) of at least 2. In an embodiment of acommercial airliner similar to that which is shown in FIGS. 1 and 2, thehigh aspect ratio wings 192 may be provided in an aspect ratio in therange of from approximately 2 to 10 or higher. Each wing 192 may have awing root 198, a wing tip 202, a leading edge 204, and a trailing edge206. The wing root 198 has a root chord 200 extending between theforward-most point on the leading edge 204 and the aft-most point on thetrailing edge 206. In the present disclosure, the wing root 198 isdefined at the intersection of the wing 192 with the fuselage 170. Inthe baseline configuration 132 of the aircraft 102 in FIG. 1, the wings192 are arranged in a bilaterally symmetric configuration 130 whereinthe wings 192 are positioned at the same station location.

In FIG. 1, the aircraft 102 may further include one or more propulsionunits 230. The aircraft 102 is shown in a twin-engine arrangement havinga pair of propulsion units 230 mounted to the wings 192 on oppositesides of the fuselage 170. The propulsion units 230 may be positioned atapproximately the same lateral location on opposite sides of thefuselage 170. In an embodiment, the air vehicle 100 (i.e., aircraft 102)may include equivalent quantities of engine nacelles 232 or propulsionunits 230 on opposing sides of the body 104. Each propulsion unit 230 ofa pair may be positioned at the same lateral location on opposite sidesof the fuselage 170. In this regard, each one of propulsion units 230 ofa pair may be mounted at approximately the same distance from thefuselage 170 on opposite sides thereof. In an embodiment not shown,uneven quantities of propulsion units 230 or engine nacelles 232 may beincluded with the aircraft 102. In addition, propulsion units 230 may bemounted at any location on the wings 192, the fuselage 170, and/or onother structures (not shown) that may be included with the aircraft 102,such that the propulsion units 230 are not limited to mounting at thelocations shown in FIG. 1. The propulsion units 230 on each side of thefuselage 170 may generally have a similar configuration although thesystem and method disclosed herein may be applied to aircraft 102 havingdifferent propulsion unit configurations.

In FIG. 1, each one of the propulsion units 230 may include enginenacelles 232 or propulsion units 230 which are shown as beingwing-mounted as distinguished from engine nacelles (not shown) orpropulsion units (not shown) that may be integrated with a fuselage (notshown). In any of the embodiments disclosed herein, engines nacelles maybe fuselage-mounted (not shown) via pylons or mounts extending outwardlyform the fuselage. In the embodiments disclosed herein, the enginenacelles 232 on each side of the fuselage 170 may have substantiallysimilar nacelle diameters, lengths, and configurations.

Each engine nacelle 232 may generally define an outer geometry of thepropulsion unit 230. In addition, each engine nacelle 232 has an engineinlet 238 which, in the present disclosure, is defined as theforward-most point and/or a front face of the engine nacelle 232. In thepresent disclosure, the engine nacelle 232 extends from the engine inletto the engine nozzle 240 defined in the present disclosure as theaft-most point and/or an aft end of the engine nacelle 232 or theaft-most point of the propulsion unit 230. In the baseline configuration132 of the aircraft 102 in FIG. 1, the wing-mounted engine nacelles 232are arranged in a bilaterally symmetric configuration 130 wherein theengine inlets 238 and the engine nozzles 240 are generally positioned atthe same station location.

Although the propulsion units 230 in the present disclosure are shownand described in the context of turbine engines having engine nacelles232, the system and method disclosed herein may be applied to aircraft102 having turboprop engines or other propeller-driven engines, and mayadditionally include piston engines, or any other type of the propulsionunit, without limitation. In addition, the system and method disclosedherein may be directed toward aircraft planforms other than thetube-and-wing aircraft 102 illustrated in FIG. 1. For example, thesystem and method disclosed herein may be directed toward blended wingaircraft or any type of air vehicle 100 or air/space vehicle, withoutlimitation, which operates at, near, or above the transonic flightregime.

Referring to FIG. 1A, shown is a section view of a local longitudinalcross-sectional area 176 of the baseline configuration 132 of theaircraft 102 taken along a cutting plane 140 passing through thefuselage 170 at a forward station location 134 as shown in FIG. 1. Thefuselage cross-sectional area 176 in FIG. 1A represents the aircraftcross-sectional area displacing an oncoming airflow stream 110 (FIG. 1).

Referring to FIG. 1B, shown is a section view of the local longitudinalcross-sectional area of the baseline configuration 132 aircraft 102taken along a cutting plane 140 at an intermediate station location 136(FIG. 1) of the aircraft 102. The cross-sectional area in FIG. 1Bincludes the cross-sectional area 176 of the fuselage 170 and thecross-sectional area 242 of both of the engine nacelles 232. In thisregard, FIG. 1B illustrates the abrupt increase in the cross-sectionalarea displacing an oncoming airflow stream 110 (FIG. 1) for aconventional baseline configuration 132 aircraft 102.

Referring to FIG. 1C, shown is a section view of the local longitudinalcross-sectional area of the baseline configuration 132 aircraft 102taken along a cutting plane 140 at an aft station location 138 (FIG. 1)of the aircraft 102. The cross-sectional area in FIG. 1C includes thecross-sectional area 176 of the fuselage 170, the cross-sectional area242 of both of the engine nacelles 232, and the cross-sectional area 208of the wing 192 on each side of the fuselage 170 at the aft stationlocation 138. FIG. 1C further illustrates the abrupt increase in thecross-sectional area occurring in a relatively short distance betweenthe intermediate station location 136 and the aft station location 138(FIG. 1) and which may correspond to a significant increase in wave dragas the baseline configuration 132 aircraft 102 approaches the speed ofsound.

Referring to FIG. 2, shown is a top view of an aircraft 102advantageously having a bilaterally asymmetric configuration 150 havingengine nacelles 232 that are longitudinally offset from one another. InFIG. 2, the engine nacelles 232 comprise a forward nacelle 234 which maybe positioned forward of the aft nacelle 236 on the opposite side of thefuselage 170. In this regard, the engine nacelles 232 in FIG. 2 may belongitudinally offset from one another by an engine offset distance asdescribed below. With the exception of the engine nacelles 232, theengine offset configuration 152 of the aircraft 102 in FIG. 2 may besubstantially similar to the baseline configuration 132 of the aircraft102 in FIG. 1 with regard to the bilateral symmetry of the remainingcomponents 114 of the aircraft 102 with regard to the protrudingaerodynamic surfaces 190 such as the wings 192, the horizontalstabilizers 268, and other components 114.

In FIG. 2, the engine nacelles 232 may be offset by an offset distance244. In the embodiment shown, the forward nacelle 234 and the aftnacelle 236 are positioned at generally the same lateral location onopposite sides of the fuselage 170. However, the forward nacelle 234 maybe positioned such that at least a portion of an approximately constantcross-sectional area 249 (i.e., illustrated in cross-hatch) of theforward nacelle 234 is generally longitudinally aligned with an engineinlet 238 (i.e., the forward face) of an aft nacelle 236. For example, alocation of a forward end 250 of an approximately constantcross-sectional area 249 of the forward nacelle 234 is generally alignedwith the engine inlet 238 of the aft nacelle 236 and which may providean offset distance 244 that corresponds to minimum wave drag for theaircraft configuration. In this regard, the forward nacelle 234 and theaft nacelle 236 may be longitudinally offset by an offset distance 244that minimizes the rate of change (e.g., increasing or decreasing) ofcross-sectional area of the aircraft relative to the rate of change ofcross-sectional area of a bilaterally symmetric aircraft. In anembodiment, the forward nacelle 234 may be positioned forward of anon-offset location (not shown) or original symmetric location of theforward nacelle 234. Likewise, the aft nacelle 236 may be positioned aftof a non-offset location (not shown) or original symmetric location ofthe aft nacelle 236. However, the forward nacelle 234 and the aftnacelle 236 may be positioned at any location relative to theirrespective non-offset locations.

In an embodiment, the engine nacelles 232 may be offset by an offsetdistance 244 that is as large as is physically practical. For example,the engine nacelles 232 may be offset by any amount ranging fromnon-offset (i.e., longitudinally aligned) up to an offset distance 244wherein the engine inlet 238 of one engine nacelle 232 is aligned withthe engine nozzle 240 of the engine nacelle 232 on an opposite side ofthe fuselage 170. Larger engine offset distances 244 are also possible.In an embodiment, the engine nacelles 232 may be longitudinally offsetsuch that at least a portion of an approximately constantcross-sectional area 249 of a forward nacelle 234 is generallylongitudinally aligned with an engine inlet of an aft nacelle 236. Theapproximately constant cross-sectional area 249 is shown in cross-hatchin FIG. 2 and may include a region of maximum cross sectional area ofthe engine nacelle 232. In this regard, the approximately constantcross-sectional area 249 of an engine nacelle 232 may have a slightlycurved outer surface (e.g., convexly curved) and is not necessarilylimited to a constant outer diameter or constant cross-sectional shape.

In the embodiment shown in FIG. 2, the station location of the engineinlet 238 (e.g., the forward face) of the aft nacelle 236 on one side ofthe fuselage 170 may be generally longitudinally aligned with an aft end251 of the approximately constant cross-sectional area 249 of theforward nacelle 234 on the opposite side of fuselage 170. In a furtherembodiment not shown, the station location of the aft end of 251 theapproximately constant cross-sectional area 249 of the aft nacelle 236may be generally longitudinally aligned with the engine nozzle 240 ofthe forward nacelle 234. In another embodiment not shown, the enginenozzle 240 of the forward nacelle 234 on one side of the fuselage 170may be generally longitudinally aligned with the engine inlet 238 of theaft nacelle 236 on the opposite side of fuselage 170. Advantageously,the above-noted positions of the forward and aft end 250, 251 of theapproximately constant cross-sectional area 249 may correspond tominimum wave drag of the aircraft 102.

In a further embodiment not shown, the engine nacelles 232 may belongitudinally offset such that a region of decreasing cross-sectionalarea of a forward nacelle 234 at least partially overlaps a region ofincreasing cross-sectional area of an aft nacelle 236. The region ofdecreasing cross-sectional area of an engine nacelle 232 may comprisethe portion of the nacelle located aft of the approximately constantcross-sectional area 249. The region of increasing cross-sectional areaof an engine nacelle 232 may comprise the portion of the nacelle locatedforward of the approximately constant cross-sectional area 249. Byoverlapping the decreasing cross-sectional of a nacelle on one side ofthe fuselage with the increasing cross-sectional area of a nacelle on anopposite side of the fuselage, the rate of change of cross-sectionalarea of the aircraft 102 may be minimized relative to an air vehiclehaving bilaterally symmetric (non-offset) engine nacelles.

For any one of the bilaterally asymmetric embodiments disclosed herein,the offset distance for a pair of components 114 (e.g., engine nacelles232, wings 192, stabilizers 268, control surfaces 272, etc.) on oppositesides of the fuselage 170 may be analytically determined according to amethod described below to calculate one or more offset distances thatcorrespond to minimum wave drag for the aircraft 102. Alternatively, theamount of offset distance may be determined experimentally, or by acombination of analysis and experimentation.

The engine offset configuration 152 in FIG. 2 represents one of avariety of bilaterally asymmetric configurations 150 that mayadvantageously minimize an increase in wave drag of an aircraft 102. Inthe present disclosure, wave drag in an air vehicle 100 mayadvantageously be minimized by mounting one or more pairs of components114 in an offset arrangement on opposite sides of the fuselage 170. Forexample, as described in greater detail below, wave drag may beminimized by longitudinally offsetting a pair of protruding aerodynamicsurfaces 190 of the aircraft 102. Protruding aerodynamic surfaces 190may be defined as any member that extends outwardly from the body 104 orfuselage 170 of the air vehicle 100 or aircraft 102.

In the present disclosure, protruding aerodynamic surfaces 190 mayinclude wings 192 such as high aspect ratio wings 192, horizontalstabilizers 268, vertical stabilizers 262, canted stabilizers (notshown), canards (not shown), control surfaces 272 such as empennagecontrol surfaces, external stores 300, and other protruding aerodynamicsurfaces 190. Stabilizers may be defined as aerodynamic surfaces thatprovide directional stability to the aircraft 102 or air vehicle 100. Inan embodiment, stabilizers may comprise fixed or non-movable protrudingaerodynamic surfaces 190. In the present disclosure, protrudingaerodynamic surfaces 190 may also comprise control surfaces 272 such asfor aerodynamic control or directional control of aircraft 102 or airvehicle 100 and may include generally movable control surfaces 272. Forexample, a control surface 272 may include a rudder, an elevator, anelevon, a ruddervator, or any one of a variety of movable surfaces. Thecontrol surface 272 may be hingedly coupled at one edge to anothermember such as a stabilizer. However, a control surface 272 may bepivotably mounted to the air vehicle 100 or aircraft 102 as a separatecomponent. For example, a control surface 272 may comprise an all-movingelevator, rudder, or other control surface configuration. In the presentdisclosure, a protruding aerodynamic surface 190 may include any member,structure, device, or component that presents a change incross-sectional area to an oncoming airflow stream 110 passing over anair vehicle 100 or aircraft 102.

Referring to FIG. 2A, shown is a section view of the local longitudinalcross-sectional area of the engine offset configuration 152 of theaircraft 102 taken along the cutting plane 140 at the forward stationlocation 154 in FIG. 2. The forward station location 154 in FIG. 2 ispositioned at the same location as the forward station location 134 inFIG. 1. The cross-sectional area 176 in FIG. 2A has the samecross-sectional area 176 as in FIG. 1A.

Referring to FIG. 2B, shown is a section view of the local longitudinalcross-sectional area of the engine offset configuration 152 taken alonga cutting plane 140 at a first intermediate station location 156 (FIG.2) of the aircraft 102. The cross-sectional area in FIG. 2B includes thecross-sectional area 176 of the fuselage 170 and the cross-sectionalarea 242 of a single one of the engine nacelles 232. In this regard,FIG. 2B illustrates a more gradual increase in the cross-sectional areafor the engine offset configuration 152 relative to the more abruptincrease in cross-sectional area shown in FIG. 1B for the baselineconfiguration 132.

Referring to FIG. 2C, shown is a section view of the local longitudinalcross-sectional area of the engine offset configuration 152 taken alonga cutting plane 140 at a second intermediate station location 157 (FIG.2). The cross-sectional area in FIG. 2C includes the cross-sectionalarea 176 of the fuselage 170 and the cross-sectional area 242 of both ofthe engine nacelles 232 and is similar in size to the cross-sectionalarea shown in FIG. 1B for the baseline configuration 132 aircraft 102 ofFIG. 1. FIG. 2C further illustrates the gradual increase incross-sectional area for the engine offset configuration 152 relative tothe abrupt increase in cross-sectional area for the baselineconfiguration 132.

Referring to FIG. 2D, shown is a section view of the local longitudinalcross-sectional area of the baseline configuration 132 aircraft 102taken along a cutting plane 140 at the aft station location 158 (FIG. 2)of the aircraft 102. The aft station location 158 in FIG. 2 is at thesame location as the aft station location 138 in FIG. 1 and thecross-sectional area 176 in FIG. 2D has the same cross-sectional area176 as in FIG. 1C. The cross-sectional area in FIG. 2D includes thecross-sectional area of the fuselage 170, the cross-sectional area 242of both of the engine nacelles 232, and the cross-sectional area 208 ofa portion of the wings 192 at the aft station location 158.

FIGS. 2A-2D illustrate the more gradual increase in cross-sectional areaachieved by longitudinally offsetting the engine nacelles 232 relativeto the abrupt increase in cross-sectional area of the baselineconfiguration 132 as shown in FIGS. 1A-1D. While not indicated in FIGS.2A-2D, the offset engine nacelles 232 may be longitudinally offset toprovide a gradual decrease in cross-sectional area as the airflow stream110 approaches the aft end of the longitudinally offset engine nacelles232. As may be appreciated, by longitudinally offsetting the enginenacelles 232, wave drag may be minimized due to the more gradual changein the distribution of the cross-sectional area along the longitudinalaxis 106 of an aircraft 102. In any of the embodiments disclosed herein,the gradual change in the distribution of the cross-sectional area mayinclude a gradual increase in cross-sectional area and/or a gradualdecrease in cross-sectional area of the air vehicle 100 or aircraft 102.

Referring to FIG. 3, shown is a graph plotting longitudinalcross-sectional area versus station location for the baselineconfiguration 132 (i.e., no offset) of FIG. 1 and for the engine offsetconfiguration 152 of FIG. 2. Station location is indicated relative toan origin 108 position which is located on the graph midway between theforward fuselage location on a left side of the graph and the aftfuselage location on a right side of the graph. The graph of FIG. 3 wasgenerated from a relatively low fidelity analysis of the baselineconfiguration 132 and a relatively low fidelity analysis of the engineoffset configuration 152 using the same analysis parameters as in thebaseline configuration 132 analysis.

In FIG. 3, the plot of the area distribution for the baselineconfiguration 132 (i.e., no offset) is illustrated as a solid line. Theplot of the area distribution for the engine offset configuration 152 isillustrated as a dashed line and is superimposed with the solid line ofthe baseline configuration 132. For the engine offset configuration 152,the dashed line of the plot illustrates an initial increase incross-sectional area at the first intermediate station location 156 andrepresents the area contribution from the forward nacelle 234 (FIG. 2).As can be seen, the initial area increase for the engine offsetconfiguration 152 occurs prior to (i.e., relative to an oncoming airflowstream) the initial increase in cross-sectional area for the baselineconfiguration 132. The difference in height of the dashed line and solidline also illustrates that the maximum cross-sectional area of theengine offset configuration 152 is less than the maximum cross-sectionalarea of the baseline configuration 132.

FIG. 4 illustrates a plot of the derivative of the area contribution ofFIG. 3 and illustrates the change in cross-sectional area versus stationlocation for the baseline configuration 132 and the engine offsetconfiguration 152. The plot of change in area distribution for thebaseline configuration 132 is shown as a solid line. The plot of changein area distribution for the engine offset configuration 152 is shown asa dashed line. The dashed line in FIG. 4 illustrates relatively uniformblending of the area contributions from the forward nacelle 234 (FIG. 2)and the aft nacelle 236 (FIG. 2) for the engine offset configuration 152and which advantageously corresponds to a minimal rate of area increase.In contrast, in the same section of the plot of FIG. 4, the solid lineillustrates an abrupt increase in area contribution (i.e., for baselineconfiguration 130 identified in FIG. 4 with reference numeral 130) fromthe longitudinally-aligned engine nacelles 232 of the baselineconfiguration 132 (FIG. 1). In addition, the negative peak in the solidline illustrates an abrupt decrease in area contribution from thelongitudinally-aligned engine nacelles 232 of the baseline configuration132.

FIG. 5 shows an aircraft 102 in a bilaterally asymmetric configuration150 having longitudinally offset protruding aerodynamic surfaces 190including longitudinally offset wings 192 and/or longitudinally offsethorizontal stabilizers 268. In the present disclosure, as indicatedabove, a protruding aerodynamic surface 190 comprises any member that ismounted to and/or extends or protrudes outwardly from the body 104. Theaircraft 102 in FIG. 5 includes a forward wing 194 and an aft wing 196which may be offset from one another by any wing offset distance,without limitation. The aircraft 102 may also include stabilizers thatmay be offset from one another by any distance, without limitation. Forexample, an aircraft 102 may include a pair of horizontal stabilizers268 such as a forward stabilizer 264 and an aft stabilizer 266 that maybe offset from one another. Although not shown, the vertical stabilizer262 or vertical tail may be longitudinally offset with respect to thehorizontal stabilizer 268. In addition to offset wings 192, an aircraft102 in a bilaterally asymmetric configuration 150 may includelongitudinally offset canard surfaces (not shown) mounted at a forwardend of a fuselage, longitudinally offset ruddervators (not shown) as maybe mounted to an aft end of a fuselage, or other empennageconfigurations (e.g., V-tail, U-tail, T-tail, etc.—not shown) that maybe offset from one another. Longitudinally offset protruding aerodynamicsurfaces 190 may also include control surfaces (not shown) that may bemounted to a blended wing aircraft (not shown).

In FIG. 5, the forward wing 194 and the aft wing 196 may belongitudinally offset from one another by any distance, as indicatedabove. The engine nacelles 232 on each side of the fuselage may bemounted at the same position relative to the wing such thatlongitudinally offsetting the wings also results in longitudinallyoffsetting the engine nacelles. However, the aircraft may be configuredwith longitudinally offset wings and non-offset wing-mounted enginenacelles (not shown). In FIG. 5, the longitudinally offset wings 192 mayhave a generally high aspect ratio of up to 10 or greater as compared toa delta wing (not shown) aircraft that may have a relatively low aspectratio of 3 or less.

In any of the offset configurations disclosed herein, a maximum offsetdistance of a set of components (engine nacelles 232, protrudingaerodynamic surfaces 190, etc.) may be dependent on the configuration ofthe air vehicle. For example, the wing offset distance on an unmannedaerial vehicle (UAV) may be less than the wing offset distance on acommercial jetliner. The maximum offset distance may be determined bystructural, aerodynamic, and/or manufacturing constraints, or otherconstraints. In FIG. 5, the forward wing 194 is shown offset from theaft wing 196 by a wing offset distance 210 of approximately a length ofthe root chord 200 of one of the wings 192. As indicated above, the wingroot 198 may be defined at a location of an intersection of the wings192 with the fuselage 170. In an embodiment, the wings 192 may be offsetfrom one another by an offset distance 210 of between approximately 1foot and a length of the root chord 200. However, in order to minimizecomplications due to load path transfers or torsional loads on thefuselage 170, or complications regarding aerodynamics, the offsetdistance 210 of a pair of offset wings 192 may be minimized.

The horizontal stabilizers 268 may also be longitudinally offset by astabilizer offset distance 270 that may be limited to the length of theroot chord 200 of one of the horizontal stabilizers 268. However, thehorizontal stabilizers 268 may be offset by any stabilizer offsetdistance 270, without limitation, as indicated above. In any embodimentdisclosed herein, the protruding aerodynamic surfaces 190 may belongitudinally offset from one another such that a region of decreasingcross-sectional area of a forward component (e.g. a forward protrudingaerodynamic surface) on one side of the fuselage at least partiallyoverlaps a region of increasing cross-sectional area of an aft component(e.g. an aft protruding aerodynamic surface) on an opposite side of thefuselage.

FIG. 6 shows a further embodiment of an aircraft 102 in a bilaterallyasymmetric configuration 150. As shown, the wings 192 may be bilaterallysymmetric such that the wings 192 are positioned at the same stationlocation on opposite sides of the fuselage 170. Bilateral asymmetry ofthe aircraft 102 may be provided with asymmetrically lengthened enginenacelles 232. In this regard, an engine nacelle 232 on one side of thefuselage 170 may be provided with a forward nacelle extension 246. Theforward nacelle extension 246 may extend or protrude forwardly from theengine nacelle 232. In addition, an engine nacelle 232 on an oppositeside of the fuselage 170 may be provided with an aft nacelle extension248. The aft nacelle extension 248 may extend or protrude aftwardly fromthe engine nacelle 232. An aircraft may include a forward nacelleextension 246 on one engine nacelle 232, and/or an aft nacelle extension248 on one nacelle. However, an aircraft may be provided with both aforward nacelle extension 246 and an aft nacelle extension 248 on oneengine nacelle 232.

As shown, the forward nacelle extension 246 may be offset by anextension offset distance 252 and/or the aft nacelle extension 248 maybe offset by an extension offset distance 252 which may be differentthan the extension offset distance 252 of the forward nacelle extension246. The embodiment shown in FIG. 6 may represent a retrofitconfiguration for an existing air vehicle 100 such as an existingaircraft 102 having a bilaterally symmetric configuration, at least withregard to the symmetry of the wings 192 and engine nacelles 232. Byadding a forward nacelle extension 246 and/or an aft nacelle extension248, wave drag characteristics of an existing aircraft 102 may besignificantly improved.

FIG. 7A shows an embodiment of a cruise missile 280 in a bilaterallysymmetric configuration 130 having a missile body 282 andlongitudinally-aligned missile wings 284. The cruise missile 280represents an alternative embodiment of an air vehicle 100 that mayoperate in the transonic region and which may benefit from the systemand method for minimizing wave drag as disclosed herein.

FIG. 7B shows the cruise missile 280 in a bilaterally asymmetricconfiguration 150 having offset missile wings 284. The missile wings 284may be offset by a missile wing offset 290 distance of up to a length ofthe root chord 288 of the missile wing root 286 although the missilewings 286 may be provided in any missile wing offset 290 distance,without limitation, as indicated above. Advantageously, the offsetmissile wings 284 may provide a more gradual change in the distributionof the cross-sectional area of the missile 280 relative to the symmetricmissile 280 configuration shown in FIG. 7A. The above-described offsetconfigurations may also be applied to a rocket (not shown) or launchvehicle. For example, a rocket may be provided with stabilizing fins(not shown) that may be offset for minimizing the wave drag. Any one ofthe above-described offset configurations may also be applied to othervehicles including space vehicles for minimizing wave drag during travelthrough the atmosphere.

FIG. 8A is a top view of an embodiment of a military aircraft 102configuration. The aircraft 102 has an equal number of external stores300 indentified as 300A, 300B, 300C, and 300D mounted in a bilaterallysymmetric configuration 130 on the aircraft 102. The external stores 300are illustrated as fuel pods 302 mounted to the wings in two pairs onopposite sides of the fuselage 170. However, the external stores 300 maybe provided in any type of store configuration that may be releasablymounted to the aircraft 102. For example, external stores 300 mayinclude, but are not limited to, weapons such as missiles and/or bombs,surveillance pods, or any other type of external store that may bereleasably mounted to the aircraft 102. The external stores 300 may bereleased from the aircraft 102 in a manner that minimizes asymmetricalloading while minimizing the rate of change of cross-sectional area ofthe aircraft 102 similar to the engine offset configuration 152illustrated in FIG. 2 and described above.

For example, FIG. 8B-8D illustrates an embodiment of a sequence forreleasing external stores 300 in a manner that minimizes cross-sectionalarea change. FIG. 8B shows the release of external store 300A prior tothe release of the external stores 300B, 300C, and 300D to effectivelyprovide a bilateral asymmetric configuration in FIG. 8B. FIG. 8Cillustrates the next stage of the release sequence wherein externalstore 300C is released prior to the release of external stores 300B and300D. The stage of the release sequence in FIG. 8C may represent anarrangement that minimizes the rate of change of the cross-sectionalarea of the aircraft 102 relative to an arrangement wherein externalstores 300 are released in equal quantities (not shown) from each sideof the aircraft 102.

FIG. 8D illustrates the next stage of the release sequence whereinexternal store 300D is released prior to external store 300B which,although not shown, is the last one of the external stores 300 to bereleased. The release sequence 300A-300C-300D-300B may provide a balancebetween aircraft stability and control concerns with reductions in wavedrag. However, other release sequences are possible that may effectivelydecrease wave drag by minimizing the rate of change in thecross-sectional area of the aircraft 102. For example, for aircraft (notshown) having more than four (4) releasable external stores 300,alternative release sequences may be configured to minimizecross-sectional area change. By releasing the external stores 300 in oneor more of the above-described manners, wave drag may be minimized whichmay improve range and/or increase air speed capability such as foroperations near or in the transonic region.

FIG. 8E illustrates an embodiment of the aircraft of FIG. 8A wherein theexternal stores 300 are loaded or mounted to the aircraft 102 in astaggered manner that may minimize the rate of change in thecross-sectional area of the aircraft 102. In contrast to the arrangementshown in FIG. 8A wherein the external stores 300A, 300B, 300C, and 300Dare mounted in a bilaterally symmetric arrangement, FIG. 8E illustratesthe external stores mounted in a bilaterally offset or staggeredarrangement. For example, in FIG. 8E, the external stores 300A and 300Dmay be offset from one another by a store offset 304. Likewise, externalstores 300B and 300C may be offset from one another by a store offset304. The offset of the external stores 300A-300D and 300B-300C mayminimize the additions and subtractions of the cross-sectional areaalong the longitudinal axis of the aircraft 102 and which mayadvantageously minimize wave drag.

FIG. 9 is a flow diagram illustrating an embodiment of a method 400 ofminimizing wave drag of an air vehicle 100. The method may include Step402 of providing a body 104 of an air vehicle 100 such as an aircraft102. As indicated above, the air vehicle 100 has a longitudinal axis 106oriented generally parallel to a forward flight direction 112. The airvehicle 100 may have aftwardly-swept fixed wings, forwardly-swept fixedwings (not shown), or unswept fixed wings (not shown). The air vehicle100 may be an aircraft 102 such as a commercial aircraft 102 asillustrated in FIGS. 2 and 11 or a military aircraft 102 as illustratedin FIG. 8B. The air vehicle 100 may also be a missile such as a cruisemissile 280 illustrated in FIG. 7B, or any one of a variety ofalternative air vehicle 100 configurations that may operate at or nearthe transonic region or at high Mach numbers.

Step 404 of the method 400 of FIG. 9 may include longitudinallyoffsetting at least one pair of components 114 on opposite sides of thebody 104. However, the present disclosure is not limited to offsettingeven numbers (e.g., pairs) of components. In this regard, the system andmethod disclosed herein may include offsetting uneven numbers ofcomponents such as offsetting three (3) or more components relative toone another to minimize a rate of change in the cross-sectional area ofan aircraft 102. As indicated above, components 114 that may be offsetmay include protruding aerodynamic surfaces 190 (FIG. 2) such as wings192 (FIG. 2), horizontal stabilizers 268 (FIG. 2), vertical stabilizers262 (FIG. 2), canted stabilizers (not shown), control surfaces 272 (FIG.2), empennage control surfaces, external stores 300, or any otherprotruding aerodynamic surfaces 190 extending outwardly from thefuselage 170 or body 104 or wings 192 of an air vehicle 100.

Components 114 may also include propulsion units 230 including enginenacelles 232 which may be wing-mounted and/or fuselage-mounted and whichmay be longitudinally offset on opposite sides of the fuselage 170 asdescribed above. In an embodiment, the method may comprise mounting apair of wings 192 in a bilaterally symmetrical manner (i.e., non-offset)on opposite sides of the body 104, and longitudinally offsetting a pairof engine nacelles 232 as shown in FIG. 2 and/or in one of theembodiments described above. Although not shown, the method may includeoverlapping a region of decreasing cross-sectional area of a forwardnacelle 234 with a region of increasing cross-sectional area of an aftnacelle 236 as described above. In one example, the method may includelocating the engine inlet 238 of an aft nacelle 236 aft of the engineinlet of the forward nacelle 234 and forward of the nozzle 240 of theforward nacelle 234. In an embodiment, the engine inlet of the aftnacelle 236 may be longitudinally positioned aft of the engine inlet 238of the forward nacelle 234 by no more than 20 percent of an enginelength 254 of the forward nacelle 234. In a further example, the engineinlet of the aft nacelle 236 may be longitudinally positioned aft of theengine inlet of the forward nacelle 234 within 8-13 percent of theengine length 254 of the forward nacelle 234, as a means to optimizetotal aircraft drag which includes wave drag such as when the aircraft102 is operating at or near the transonic regime. Further examples aredescribed below for longitudinally positioning the aft nacelle 236relative to the forward nacelle 234.

In an embodiment, an existing bilaterally symmetric air vehicle 100 maybe converted to a bilaterally asymmetric air vehicle 100 by addingextensions to one or more components 114 of the air vehicle 100 toachieve an offset arrangement. For example, bilateral asymmetry may beachieved by retrofitting an existing aircraft 102 or airplane to add aforward nacelle extension 246 to an engine nacelle 232 on one side ofthe fuselage 170, and/or add an aft nacelle extension 248 to an enginenacelle 232 on an opposite side of the fuselage 170 as shown in FIG. 6.The forward nacelle extension 246 and/or the aft nacelle extension 248may be offset by an extension offset distance 252 as mentioned above. Asmay be appreciated, other extension configurations may be added to othercomponents 114 of an existing aircraft 102 to achieve bilateralasymmetry and improve the cross-sectional area distribution along alongitudinal axis 106 of the aircraft 102.

Bilateral asymmetry may also be achieved in a bilaterally symmetric airvehicle 100 (e.g., the aircraft of FIG. 8A) by the manner in whichexternal stores 300 (e.g., a missile 280, a bomb, and a fuel pod 302)are released from the aircraft 102. For example, as indicated above withregard to FIGS. 8A-8D, bilateral asymmetry may be effectively providedby releasing external stores 300 in a sequence that minimizes the changein the cross-sectional area of the aircraft (FIG. 8B) and which maypreferably minimize total configuration drag of the aircraft. Theexternal stores 300 may be mounted in a bilaterally symmetrical manneron opposite sides of a body 104 (e.g., fuselage). Longitudinal asymmetrymay be achieved by releasing one or more external stores 300 on one sideof the body 104 prior to releasing one or more external stores on anopposite side of the body 104. Total configuration drag may includeparasite drag (including interference drag), pressure drag, and wavedrag. Referring to FIG. 8E, bilateral asymmetry may also be provided bymounting external stores 300 with store offsets 304 as described aboveas a means to minimize changes in the cross-sectional area of theaircraft 102 which may minimize wave drag.

Step 406 of the method 400 of FIG. 9 includes minimizing a rate ofchange in the cross-sectional area of the air vehicle or aircraft inresponse to longitudinally offsetting the components. The longitudinaloffsetting of the components results in a bilaterally asymmetricconfiguration. In any of the embodiments disclosed herein, bilateralasymmetry may be implemented in a manner that minimizes totalconfiguration drag or total aircraft drag. Minimizing totalconfiguration drag may include a reduction in wave drag relative to thewave drag of a bilaterally symmetric configuration. However, minimizingtotal configuration drag may result in a reduced wave drag that may notbe reduced to an absolute minimum.

The method of minimizing wave drag may include estimating the wave dragof an air vehicle 100 as a means to determine an optimal offset distancebetween a pair of components 114 mounted on opposite sides of the body104 of the air vehicle 100. In this regard, the minimum wave dragcorresponds to at least one nominal offset between the components 114.The wave drag of an air vehicle 100 may be represented by the dragcoefficient (C_(D)) of the air vehicle 100 at a given Mach number. Thewave drag coefficient of an air vehicle 100 may be estimated bycalculating the cross-sectional area distribution S(x) of the airvehicle 100 over a vehicle length l_(v) as illustrated in FIG. 3. Basedon the area distribution, the method may include calculating the rate ofchange of the cross-sectional area distribution S′(x) over the vehiclelength l_(v). The graph of FIG. 4 plots the rate of change ofcross-sectional area distribution S′(x) over the vehicle length l_(v).As shown in FIG. 3, the area distribution S(x) may be centered withreference to an origin 108 located midway between the forward and aftends of the air vehicle 100. The area distribution S(x) may be convertedto a function of φ wherein:

$x = {\frac{l_{v}}{2}\cos\;\phi}$

The method may then include calculating a Fourier series expansion ofthe cross-sectional area distribution S(x) using the following equation:

${S^{\prime}(\phi)} \cong {\sum\limits_{n = 1}^{n_{\max}}{b_{n}{\sin\left( {n\;\phi} \right)}}}$${{wherein}:b_{n}} = {\frac{2}{\pi}{\int_{0}^{\pi}{{S^{\prime}(\phi)}{\sin\left( {n\;\phi} \right)}{\mathbb{d}\phi}}}}$

The wave drag may be estimated using the following relation for the wavedrag coefficient C_(D):

$C_{D} = {\frac{\pi}{4S}{\sum\limits_{n = 1}^{n_{\max}}{n\; b_{n}^{2}}}}$

wherein n_(max) represents a quantity of Fourier terms that results inconvergence of the Fourier series. The above described method ofestimating wave drag is disclosed in NASA Technical Note D-446 (1960)entitled “Some Examples of the Applications of the Transonic andSupersonic Area Rules to the Prediction of Wave Drag” by R. Nelson etal., and in NACA Technical Report 1284 (1956) entitled “Theory ofWing-Body Drag at Supersonic Speeds” by R. Jones.

The method may further include iteratively adjusting the offset distanceand estimating the resulting wave drag coefficient such as by using theabove-described method until at least one offset distance is determinedwhere the wave drag is minimized for a given aircraft 102 configuration.In this regard, aircraft 102 components 114 such as the engine nacelles232 may be offset within a range of offset distances that may yield twoor more locations where wave drag is minimized, as indicated by thelocal minima 216 in the graph of FIG. 10.

FIG. 10 is a graph plotting a drag coefficient ratio 214 of wave dragcoefficient/minimum drag versus offset distance 212 as a percentage of amaximum offset distance for several bilaterally asymmetricconfigurations 150 of an aircraft 102. The drag coefficient for each oneof the configurations was calculated using a quantity of Fourier termsof n_(max)=200. The configurations include wings 192 with offset 210(FIG. 5), propulsion units 230 (engines) with offset 244 (FIG. 2), andengine nacelles 232 with offset nacelle extensions 248 with aft offsetdistance 252 (FIG. 6), wherein the drag coefficient ratio 214 for eachconfiguration is plotted as a function of offset distance 212 as apercentage of maximum offset. For each one of the aircraft 102configurations, FIG. 10 illustrates local minima 216 for at least twooffset distances 212. Although FIG. 10 only plots the drag coefficientratio 214 for the entire length of the maximum offset for the wings 192with offset 210, the plots for the propulsion units 230 (engines) withoffset 244 and engine nacelle 232 with offset nacelle extensions 248with aft offset distance 252 are similar to the wings 192 with offsetdistance 210 and may have local minima at similar locations as theoffset wings 192 with offset distance 210.

In FIG. 10, each one of the minima 216 represents an offset distance 212(e.g., percentage) that minimizes the rate increase in cross-sectionalarea distribution. For example, for the engine offset configuration 152,a local minima 216 of the drag coefficient ratio 214 occurs at an offsetdistance 212 of approximately 20 percent of a maximum offset and whichcorresponds to the offset arrangement illustrated in FIG. 2. FIG. 10also illustrates a local minima 216 of the drag coefficient ratio 214 atan offset distance 212 of approximately 78 percent and which correspondsto an engine offset embodiment (not shown) wherein a region ofdecreasing cross-sectional area of a forward nacelle 234 (FIG. 2)overlaps a region of increasing cross-sectional area of an aft nacelle236 (FIG. 2) on the opposite side of the fuselage 170.

FIG. 10 further illustrates that for a generally bilaterally symmetricaircraft 102, adding a forward nacelle extension 246 and/or an aftnacelle extension 248 may provide a cost-effective manner for achievingbilateral asymmetry and reducing wave drag. In this regard, an existingaircraft 102 configuration may be retrofitted without significantalteration of the structural loading of the aircraft 102.Advantageously, nacelle extensions represent a means for modifying anexisting aircraft 102 to fly at higher speeds with relatively minorredesign. In this regard, the various embodiments disclosed hereinprovide a means for adjusting the longitudinal location of thecomponents 114 (e.g., wings, engines, stabilizers, control surfaces,etc.) of an aircraft 102 to improve the existing cross-sectional areadistribution without changing the local diameter of the fuselage, andwithout the use of airfoils that are tailored for the transonic flightregime.

FIG. 11 shows a further example of an aircraft 102 in a bilaterallyasymmetric configuration having longitudinally offset engine nacelles232. The aircraft 102 represents one example of an air vehicle having abody 104 (e.g., a fuselage 170) including a longitudinal axis 106continuously oriented parallel to a forward flight direction 112 whenthe air vehicle 100 is in flight. In FIG. 11, the engine inlet 238 ofthe aft nacelle 236 may be located aft of the engine inlet 238 of theforward nacelle 234 and forward of the nozzle 240 of the forward nacelle234. In some examples, the engine nacelles 232 may be longitudinallyoffset such that the region of decreasing cross-sectional area of theforward nacelle 234 overlaps a region of increasing cross-sectional areaof an aft nacelle 236.

In the embodiment shown in FIG. 11, the engine inlet 238 of the aftnacelle 236 may be located aft of the engine inlet 238 of the forwardnacelle 234 by no more than 20 percent of an engine length 254 of theforward nacelle 234. In still other examples, the engine inlet 238 ofthe aft nacelle 236 may be located aft of the engine inlet 238 of theforward nacelle 234 by no more than 10 percent of the engine length 254of the forward nacelle 234. The engine length 254 of the forward nacelle234 may be described as the distance from the engine inlet 238 of theforward nacelle 234 to the nozzle 240 of the forward nacelle 234. Theengine length 254 of the forward nacelle 234 on one side of the fuselage170 may be equivalent to the engine length 254 of the aft nacelle 236 onan opposite side of the fuselage 170. Longitudinally offsetting theforward nacelle 234 and the aft nacelle 236 by no more than 20 percentof the forward nacelle 234 engine length may represent an offset rangefor minimum overall aircraft drag such as for existing engine geometriesand for future engine geometries. Longitudinally offsetting the forwardnacelle 234 and the aft nacelle 236 by no more than 10 percent mayrepresent an offset range for minimum total drag for future enginegeometries such as engine geometries having an engine inlet of reducelength relative to existing engine geometries. The location for minimumtotal drag may be described as the engine offset location at whichoverall aircraft drag is minimized. Minimum wave drag may be describedas the engine offset location at which the wave drag component isminimized. In this regard, the location for minimum wave drag maygenerally be at a larger offset that the location for minimum totaldrag.

As indicated above, for a bilaterally asymmetric aircraft 102 withlongitudinally offset engine nacelles 232, the wings 192 may beaftwardly-swept (FIGS. 2 and 11), or the wings 192 may be non-swept (notshown) or forwardly-swept (not shown). In addition, the wings 192 may betapered and may be provided in a high aspect ratio of semi-span to chord(e.g., average chord of the semi-span). However, the wings 192 may alsobe non-tapered (not shown) wherein the airfoil section or chord may begenerally constant along a semi-span of each wing 192.

In some examples, the aft nacelle 236 engine inlet 238 may be positionedlongitudinally aft of the forward nacelle 234 engine inlet 238 withinapproximately 1-16 percent of the forward nacelle 234 engine length 254.In such an arrangement, the aft nacelle 236 engine inlet 238 may belongitudinally aligned with a location that is aft of the forwardnacelle 234 engine inlet 238 by 1-16 percent of the forward nacelle 234engine length 254. Such a longitudinal offset (e.g., 1-16 percent) mayrepresent a location for minimum total drag generated by a generic,conventional, twin-engine aircraft configuration. In other examples, theaft nacelle 236 engine inlet 238 may be located aft (e.g.,longitudinally offset) of the forward nacelle 234 engine inlet 238within a range of approximately 3-13 percent of the engine length 254 ofthe forward nacelle 234, which may represent an offset range for minimumtotal drag generated by a specific twin-engine configuration, such as atwin-engine commercial transport aircraft. In still further examples,the aft nacelle 236 engine inlet 238 may be located aft (e.g.,longitudinally offset) of the forward nacelle 234 engine inlet 238within a range of approximately 7-12 percent of the engine length 254 ofthe forward nacelle 234, which may represent an offset range for minimumwave drag for a generic, conventional, twin-engine configuration.

In a still further example, the aft nacelle 236 engine inlet 238 may bepositioned longitudinally aft of the forward nacelle 234 engine inlet238 within approximately 9-11 percent of the forward nacelle 234 enginelength 254. An offset range of 9-11 percent may represent a location forminimum wave drag for a specific twin-engine aircraft configuration,such as a twin-engine, twin-aisle commercial transport aircraft. In aspecific embodiment, the aft nacelle 236 engine inlet 238 may bepositioned longitudinally aft of the forward nacelle 234 engine inlet238 by a distance of approximately 11 percent of the forward nacelle 234engine length 254, which may represent a location for minimum wave dragfor a specific twin-engine configuration, such as a twin-aisle (e.g.,wide body) commercial transport aircraft with twin turbofan engines. Anengine offset of 11 percent may provide an approximate ⅔ reduction inthe wave drag of the engines.

As indicated above, the aircraft 102 with longitudinally offset enginenacelles 232 may include wing-mounted engines (e.g., propulsion units230) mounted on opposite sides of the fuselage 170 (e.g., the body 104).However, any one of the above-described examples may includefuselage-mounted engines located on opposite sides of the fuselage 170.In some embodiments, an aircraft 102 having longitudinally offset enginenacelles 232 may include a pair of engines, with one engine (e.g.,wing-mounted or fuselage-mounted) being located on each side of thefuselage 170. In other embodiments, an aircraft 102 havinglongitudinally offset engine nacelles 232 may include more than oneengine on each side of the fuselage 170. For example, an aircraft 102may include a pair of engines mounted on each side of the fuselage 170(e.g., wing-mounted and/or fuselage-mounted). The above-describedlongitudinally offset engine nacelle embodiments are not limited toaircraft, and may also encompass other air vehicle configurationsincluding, but not limited to, rockets and space vehicles.

Additional modifications and improvements of the present disclosure maybe apparent to those of ordinary skill in the art. Thus, the particularcombination of parts described and illustrated herein is intended torepresent only certain embodiments of the present disclosure and is notintended to serve as limitations of alternative embodiments or deviceswithin the spirit and scope of the disclosure.

What is claimed is:
 1. An air vehicle having a bilaterally asymmetricconfiguration, comprising: a body having forwardly-swept fixed wings orunswept fixed wings, the body having a longitudinal axis continuouslyoriented parallel to a forward flight direction when the air vehicle isin flight; and at least one of the following components being mounted onopposite sides of the body: longitudinally offset engine nacelles;asymmetrically lengthened engine nacelles; and longitudinally offsetprotruding aerodynamic surfaces comprising at least one of stabilizers,canards, empennage control surfaces, external stores, and high aspectratio wings.
 2. The air vehicle of claim 1, wherein: the engine nacellesare wing-mounted.
 3. The air vehicle of claim 1, wherein: an engineinlet of an aft nacelle is aft of the engine inlet of a forward nacelleand forward of a nozzle of the forward nacelle; and the forward nacelleand the aft nacelle being either the longitudinally offset enginenacelles or the asymmetrically lengthened engine nacelles.
 4. The airvehicle of claim 1, wherein: a region of decreasing cross-sectional areaof a forward nacelle overlaps a region of increasing cross-sectionalarea of an aft nacelle; and the forward nacelle and the aft nacellebeing either the longitudinally offset engine nacelles or theasymmetrically lengthened engine nacelles.
 5. The air vehicle of claim1, wherein the asymmetrically lengthened engine nacelles comprise atleast one of: a forward nacelle extension mounted to an engine nacelleon one side of the body; and an aft nacelle extension mounted to anengine nacelle on an opposite side of the body.
 6. The air vehicle ofclaim 1, wherein: the air vehicle comprises an airplane.
 7. The airvehicle of claim 1, wherein: the air vehicle comprises at least one of amissile, a rocket, and a space vehicle.
 8. An air vehicle having abilaterally asymmetric configuration, comprising: a body having fixedwings and a longitudinal axis continuously oriented parallel to aforward flight direction when the air vehicle is in flight; a forwardnacelle and an aft nacelle mounted on opposite sides of the body; and anengine inlet of the aft nacelle being located aft of the engine inlet ofthe forward nacelle by no more than 20 percent of an engine length ofthe forward nacelle.
 9. The air vehicle of claim 8, wherein: the engineinlet of the aft nacelle is located aft of the engine inlet of theforward nacelle by no more than 10 percent of the engine length of theforward nacelle.
 10. A method of minimizing wave drag of an air vehicle,comprising the steps of: providing a body of an air vehicle havingforwardly-swept fixed wings or unswept fixed wings, the body having alongitudinal axis continuously oriented parallel to a forward flightdirection when the air vehicle is in flight; and longitudinallyoffsetting at least one of the following components on opposite sides ofthe body: engine nacelles; and protruding aerodynamic surfacescomprising at least one of stabilizers, canards, empennage controlsurfaces, external stores, and high aspect ratio wings.
 11. The methodof claim 10, wherein: the engine nacelles are wing-mounted.
 12. Themethod of claim 10, wherein the step of longitudinally offsetting theengine nacelles comprises: locating an engine inlet of an aft nacelleaft of the engine inlet of a forward nacelle and forward of a nozzle ofthe forward nacelle.
 13. The method of claim 10, wherein the step oflongitudinally offsetting the engine nacelles comprises: overlapping aregion of decreasing cross-sectional area of a forward nacelle with aregion of increasing cross-sectional area of an aft nacelle.
 14. Themethod of claim 10, wherein the step of longitudinally offsetting theengine nacelles comprises at least one of: adding a forward nacelleextension to an engine nacelle on one side of the body of an existingair vehicle; and adding an aft nacelle extension to an engine nacelle onan opposite side of the body of the existing air vehicle.
 15. The methodof claim 10, wherein the step of longitudinally offsetting thestabilizers comprises: longitudinally offsetting at least one ofhorizontal stabilizers and vertical stabilizers.
 16. The method of claim10, wherein the step of longitudinally offsetting the external storescomprises: mounting external stores in a bilaterally symmetrical manneron opposite sides of the body; and releasing an external store on oneside of the body prior to releasing an external store on an oppositeside of the body.
 17. The method of claim 16 wherein at least one of theexternal stores comprises at least one of: a missile, a bomb, and a fuelpod.
 18. The method of claim 10, wherein: the air vehicle comprises anairplane.
 19. A method of minimizing wave drag of an air vehicle,comprising the steps of: providing a body having fixed wings and alongitudinal axis continuously oriented parallel to a forward flightdirection when the air vehicle is in flight; mounting a forward nacelleand an aft nacelle on opposite sides of the body; and locating an engineinlet of the aft nacelle aft of the engine inlet of the forward nacelleby no more than 20 percent of an engine length of the forward nacelle.20. The method of claim 19, wherein the step of locating the engineinlet comprises: locating the engine inlet of the aft nacelle aft of theengine inlet of the forward nacelle by no more than 10 percent of theengine length of the forward nacelle.